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January 2009Is 0 * Infinity = 1?Various mathematicians have, in a variety of ways, attempted to prove that Infinity x 0 = 1. The theory behind this is that if 1 / 0 = Infinity is true, then 0 * Infinity = 1 must also be true. Here is where our opinions differ, at least where applied to physics... Taking the null view of zero, this is never the case, no matter which interpretation of infinity you use; if zero is the absence of any value, then the result is null (or zero, if you prefer). For convenience, we categorise infinities into a number of types:
Type 2 Infinities occur only when using the { 0 } view of zero, not with the { } view of zero. When using nulls, we deal only with Types 1 and 3 (how long is a piece of string, the number of odd integers or similar values). Taking the null view of zero ( meaning nothing or the empty set { } ) then:
Zero means a value is null or "missing" and the result is therefore incomplete.
If it's mathematics then why is there argument?This is another example where our inherited, but unproven, assumptions in mathematics cause much wailing and gnashing of teeth as we attempt to shoehorn mutually incompatible views of infinity and zero into the same boot. We often find arguments about topics such as zero and infinity in mathematics because our conventional "rules" don't spell out things like varying definitions of infinity or differing views and uses of zero. Many of our views about zero came from India at least 1500 years ago. Our inherited rules frequently fail to differentiate between ordinal uses of zero (as in counting down 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0) and the use of zero as a quantity (which may be null or the absence of any value).
Regards, AJ Corcoran
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